Matching Parity of Two Dice

Each die is equally likely to land on an odd or an even face.

Condition on the parity of the first die and match the second die to it.

1. 1. Condition on the first die

   The first die is odd or even with probability $1/2$ each, by symmetry.

   $$P(\text{odd})=P(\text{even})=\frac{1}{2}$$

2. 2. Match the second die

   Given the first die's parity, the second die matches it with probability $1/2$, so the two events combine to give $1/2$ overall.

   $$P(\text{same parity})=\frac{1}{2}$$

Answer: 1/2